The resultant resistance value of n resistance each of r ohms and connected is series is X. When those n , resistance are connected in parallel , the resultant values is .

Options

A. `(x)/(n)`
B. `(x)/(n^(2))`
C. `n^(2)x`
D. `n x`

Answer

To solve the problem, we need to find the resultant resistance when n resistors, each of resistance r ohms, are connected in series and then in parallel.

### Step-by-Step Solution:

1. **Understanding Series Connection:**
When n resistors are connected in series, the total or equivalent resistance (X) is the sum of the individual resistances.
\[ X = R_1 + R_2 + R_3 + ... + R_n = nR \]
Here, since each resistor has the same resistance \( r \), we can write:
\[ X = nR \]

2. **Finding Resistance (r):**
From the equation \( X = nR \), we can express \( R \) in terms of \( X \) and \( n \):
\[ R = \frac{X}{n} \]
This is our **Equation 1**.

3. **Understanding Parallel Connection:**
When the same n resistors are connected in parallel, the formula for the equivalent resistance \( R_{eq} \) is given by:
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... + \frac{1}{R_n} \]
Since all resistors have the same resistance \( R \):
\[ \frac{1}{R_{eq}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} + ... + \frac{1}{R} = \frac{n}{R} \]
Thus, we can write:
\[ R_{eq} = \frac{R}{n} \]

4. **Substituting for R:**
Now, substituting \( R \) from **Equation 1** into the parallel resistance formula:
\[ R_{eq} = \frac{\frac{X}{n}}{n} = \frac{X}{n^2} \]

5. **Final Result:**
Therefore, the resultant resistance when the n resistors are connected in parallel is:
\[ R_{eq} = \frac{X}{n^2} \]

### Conclusion:
The resultant resistance when n resistors of r ohms each are connected in parallel is \( \frac{X}{n^2} \).